If Px-y divides Ax1- y1 and Bx2- y2 in the ratio m - n- then- Px-y - mx2-nx1-m-n-my2-ny1-m-n-

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Standard IX

Mathematics

Equal Intercept Theorem

If Px,y divid...

Question

If P(x,y) divides A $(x_{1}, y_{1})$ and B $(x_{2}, y_{2})$ in the ratio m : n, then, P(x,y) = $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$ .

False

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True

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Solution

The correct option is B True

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Similar questions

The coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) externally in the ratio m : n are given by

Let $P (x_{1}, y_{1}, z_{1})$ and $Q (x_{2}, y_{2}, z_{2})$ be two points and let R(x, y, z) be a point on PQ dividing it in the ratio m:n. Prove that
$x = \frac{m x_{2} + n x_{1}}{m + n}, y = \frac{m y_{2} + n y_{1}}{m + n}$ and $z = \frac{m z_{2} + n z_{1}}{m + n}$ .

Which of the follwing statements are correct ?
1. The coordinates of the point R which divides the line

segment joining two points $P (x_{1}, y_{1}, z_{1})$ and $Q (x_{2}, y_{2}, z_{2})$

externally in the ratio m:n are $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}, \frac{m z_{2} + n z_{1}}{m + n})$ .

2. If R divides PQ internally in the ratio m:n, then its coordinates

are obtained by replacing n by -n in the statement 1.

Q. Assertion :STATEMENT- 1 : A straight line passing through the origin intersects the branches of the hyperbola xy = 9 at Q in the first and R in the third quadrant. The point P divides the segment QR internally in the ratio 1:2, then the locus of P is ellipse Reason: STATEMENT- 2 :

A \equiv (x_{1}, y_{1}), B \equiv (x_{2}, y_{2})

If P divides line joining Aand B in the ratio m : n, then co-ordinates of P are

[\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}]

Q. If

A (x_{1}, y_{1}, z_{1})

and

B (x_{2}, y_{2}, z_{2})

are two points such that the direction cosines of

¯ A B

are

l

m

n

then

l = \frac{x_{2} - x_{1}}{∣ ∣ ¯ A B ∣ ∣}

m = \frac{y_{2} - y_{1}}{∣ ∣ ¯ A B ∣ ∣}

n = \frac{z_{2} - z_{1}}{∣ ∣ ¯ A B ∣ ∣}

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If P(x,y) divides A(x1,y1) and B(x2,y2) in the ratio m : n, then, P(x,y) = (mx2+nx1m+n,my2+ny1m+n).

The correct option is B True

If P(x,y) divides A $(x_{1}, y_{1})$ and B $(x_{2}, y_{2})$ in the ratio m : n, then, P(x,y) = $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$ .